The number of numbers between 2000 and 5000 that can be formed with the digits 0,1 , 2, 3, 4 (repetition of…
The number of numbers between 2000 and 5000 that can be formed with the digits 0,1 , 2, 3, 4 (repetition of digits not allowed) and are multiple of 3 is
48
30
24
32
Solution
Number between 2000 and 5000 is a 4 digits number.
For the multiples of 3, the sum of digit must be divisible by 3 .
There are only 2 ways of selecting the digits so that 4 digit number with the given digits can be formed, i.e. 0, 1, 2, 3 and 0, 2, 3, 4 .
The number of ways of forming number with digit $0,1,2,3$ is $2 \times 3$ ! $\quad[\because 0$ and 1 cannot be place on thousand place]
The number of ways of forming number with the digit $0,2,3,4$ is $3 \times 3 ! \quad[\because 0$ cannot be place on thousand digit]
Hence, the required number of ways
$
\begin{aligned}
& =2 \times 3 !+3 \times 3 ! \\
& =3 !(2+3)=6 \times 5=30
\end{aligned}
$